For the posited logistic regression model, we follow [1]} and take a default prior distribution for \((\beta _0, \beta _1)\)  to be
\( \pi (\beta _0,\beta _1)=\hat{b}^{-1} \exp \lbrace \beta _0 - \hat{b}^{-1} e^{\beta _0} \rbrace , \) 
